---
name: "iparmq"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/iparmq/3lapack"
---

# iparmq(3lapack)

This program sets problem and machine dependent parameters useful for xHSEQR and its subroutines

## NAME

IPARMQ - This program sets problem and machine dependent parameters  useful for xHSEQR and its subroutines

## SYNOPSIS

- INTEGER FUNCTION

  IPARMQ( ISPEC, NAME, OPTS, N, ILO, IHI, LWORK )

- INTEGER

  IHI, ILO, ISPEC, LWORK, N

- CHARACTER

  NAME\*( \* ), OPTS\*( \* )

## PURPOSE

     This program sets problem and machine dependent parameters\
      useful for xHSEQR and its subroutines. It is called whenever \
      ILAENV is called with 12 \<= ISPEC \<= 16\

## ARGUMENTS

- ISPEC (input) integer scalar

  ISPEC specifies which tunable parameter IPARMQ should return. ISPEC=12: (INMIN)  Matrices of order nmin or less are sent directly to xLAHQR, the implicit double shift QR algorithm.  NMIN must be at least 11. ISPEC=13: (INWIN)  Size of the deflation window. This is best set greater than or equal to the number of simultaneous shifts NS. Larger matrices benefit from larger deflation windows. ISPEC=14: (INIBL) Determines when to stop nibbling and invest in an (expensive) multi-shift QR sweep. If the aggressive early deflation subroutine finds LD converged eigenvalues from an order NW deflation window and LD.GT.(NW\*NIBBLE)/100, then the next QR sweep is skipped and early deflation is applied immediately to the remaining active diagonal block.  Setting IPARMQ(ISPEC=14) = 0 causes TTQRE to skip a multi-shift QR sweep whenever early deflation finds a converged eigenvalue.  Setting IPARMQ(ISPEC=14) greater than or equal to 100 prevents TTQRE from skipping a multi-shift QR sweep. ISPEC=15: (NSHFTS) The number of simultaneous shifts in a multi-shift QR iteration. ISPEC=16: (IACC22) IPARMQ is set to 0, 1 or 2 with the following meanings. 0:  During the multi-shift QR sweep, xLAQR5 does not accumulate reflections and does not use matrix-matrix multiply to update the far-from-diagonal matrix entries. 1:  During the multi-shift QR sweep, xLAQR5 and/or xLAQRaccumulates reflections and uses matrix-matrix multiply to update the far-from-diagonal matrix entries. 2:  During the multi-shift QR sweep. xLAQR5 accumulates reflections and takes advantage of 2-by-2 block structure during matrix-matrix multiplies. (If xTRMM is slower than xGEMM, then IPARMQ(ISPEC=16)=1 may be more efficient than IPARMQ(ISPEC=16)=2 despite the greater level of arithmetic work implied by the latter choice.)

- NAME (input) character string

  Name of the calling subroutine

- OPTS (input) character string

  This is a concatenation of the string arguments to TTQRE.

- N (input) integer scalar

  N is the order of the Hessenberg matrix H.

- ILO (input) INTEGER

  IHI     (input) INTEGER It is assumed that H is already upper triangular in rows and columns 1:ILO-1 and IHI+1:N.

- LWORK (input) integer scalar

  The amount of workspace available.

## FURTHER DETAILS

     Little is known about how best to choose these parameters.\
      It is possible to use different values of the parameters\
      for each of CHSEQR, DHSEQR, SHSEQR and ZHSEQR.\
\
      It is probably best to choose different parameters for\
      different matrices and different parameters at different\
      times during the iteration, but this has not been\
\
      implemented --- yet.\
\
      The best choices of most of the parameters depend\
\
      in an ill-understood way on the relative execution\
\
      rate of xLAQR3 and xLAQR5 and on the nature of each\
\
      particular eigenvalue problem.  Experiment may be the\
      only practical way to determine which choices are most\
      effective.\
\
      Following is a list of default values supplied by IPARMQ.\
      These defaults may be adjusted in order to attain better\
      performance in any particular computational environment.\
      IPARMQ(ISPEC=12) The xLAHQR vs xLAQR0 crossover point.\
                       Default: 75. (Must be at least 11.)\
      IPARMQ(ISPEC=13) Recommended deflation window size.\
\
                       This depends on ILO, IHI and NS, the\
                       number of simultaneous shifts returned\
                       by IPARMQ(ISPEC=15).  The default for\
                       (IHI-ILO+1).LE.500 is NS.  The default\
                       for (IHI-ILO+1).GT.500 is 3\*NS/2.\
\
      IPARMQ(ISPEC=14) Nibble crossover point.  Default: 14.\
      IPARMQ(ISPEC=15) Number of simultaneous shifts, NS.\
\
                       a multi-shift QR iteration.\
\
                       If IHI-ILO+1 is ...\
\
                       greater than      ...but less    ... the\
                       or equal to ...      than        default is\
                               0               30       NS =   2+\
                              30               60       NS =   4+\
                              60              150       NS =  10\
                             150              590       NS =  \*\*\
                             590             3000       NS =  64\
                            3000             6000       NS = 128\
                            6000             infinity   NS = 256\
                   (+)  By default matrices of this order are\
                        passed to the implicit double shift routine\
                        xLAHQR.  See IPARMQ(ISPEC=12) above.   These\
                        values of NS are used only in case of a rare\
                        xLAHQR failure.\
\
                   (\*\*) The asterisks (\*\*) indicate an ad-hoc\
                        function increasing from 10 to 64.\
      IPARMQ(ISPEC=16) Select structured matrix multiply.\
\
                       (See ISPEC=16 above for details.)\
\
                       Default: 3.\